1.4 Financial applications of geometric sequences and seriesIB Maths: Applications and Interpretation SL: Subtopic test

1. 1
   Mia invests 5000 EUR in an account that pays 3% interest per year, compounded annually.

   (a)

   Find the value of the investment after 8 years, to the nearest cent.

   [1 mark]

   • A$6333.85$ EUR
   • B$6200.00$ EUR
   • C$6523.87$ EUR
   • D$5121.27$ EUR

   (b)

   Suppose the same nominal annual rate of 3% were compounded quarterly. Find the value after 8 years, to the nearest cent.

   [1 mark]

   • A$6333.85$ EUR
   • B$6350.56$ EUR
   • C$5307.99$ EUR
   • D$12\,875.41$ EUR

   (c)

   Find the least number of complete years for the investment to exceed 7000 EUR.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A car costs 24 000 EUR when new. Its value depreciates by 12% each year.

   (a)

   Find the value of the car after 5 years, to the nearest cent.

   [1 mark]

   • A$42\,296.20$ EUR
   • B$9600.00$ EUR
   • C$12\,665.57$ EUR
   • D$11\,145.70$ EUR

   (b)

   Find the least number of complete years after which the value of the car is below 8000 EUR.

   [1 mark]

   • A$8$
   • B$6$
   • C$10$
   • D$9$

   (c)

   Find the total fall in the value of the car over the first 5 years, as a percentage of its price when new. Give your answer to 3 significant figures.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Karim deposits 8000 AED in a bank account that pays a nominal annual interest rate of 2.4%, compounded monthly. The average rate of inflation is 1.8% per year. Use your GDC finance application where helpful.

   (a)

   Find the value of the account after 6 years, to the nearest cent.

   [3 marks]

   (b)

   Find the real value of the account after 6 years, in today's money, to the nearest cent, and comment on what your answer shows.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A company buys a machine for 20 000 EUR. The machine loses 15% of its value each year. In 6 years' time the company will replace it with a new machine costing 20 000 EUR. It invests a lump sum today in an account paying a nominal annual interest rate of 4.2%, compounded quarterly. Use your GDC finance application where helpful.

   (a)

   (i) The company invests enough so that the account holds exactly 20 000 EUR in 6 years. Find the lump sum.
   (ii) Instead the company invests 15 000 EUR. Find the least number of complete years until the account holds at least 20 000 EUR.
   Give money answers to 2 decimal places.

   [6 marks]

   (b)

   The company sells the old machine after 6 years for its depreciated value.
   (i) Find the value of the old machine after 6 years.
   (ii) Find the extra money needed to buy the new machine.
   (iii) Find the lump sum that must be invested today to provide this extra money in 6 years.
   (iv) State one assumption of this model.
   Give money answers to 2 decimal places.

   [6 marks]

   Total for question 4: 12 marks

End of questions